Question

Pounds of allloy containing 34%cooper Pounds of alloy containing 48%copper

Answer 1

Pounds of alloy containing 34% copper = 36.14 pounds

Pounds of alloy containing 48% copper = 46-36.14=9.86 pounds

Step-by-step explanation:

The required alloy is 46 pounds of a 37% copper alloy.

• Let the pounds of 34% copper needed = x pounds

,

• Therefore, the pounds of 48% copper needed = (46-x) pounds

Multiplying the percentage by weight in each case:

`\begin{gathered} (34\%\text{ of x)+\lbrack}48\%\text{ of (46-x)\rbrack}=37\%\text{ of 46} \\ \implies0.34x+0.48(46-x)=0.37*46 \end{gathered}`

We solve for x:

`\begin{gathered} 0.34x+22.08-0.48x=17.02 \\ 0.34x-0.48x=17.02-22.08 \\ -0.14x=-5.06 \\ (-0.14x)/(-0.14)=(-5.06)/(-0.14) \\ x=36.14\text{ pounds} \end{gathered}`

Therefore:

• Pounds of alloy containing 34% copper = 36.14 pounds

,

• Pounds of alloy containing 48% copper = 46-36.14=9.86 pounds